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4Q                         ANALYTICAL MECHANICS
4.  A body is suspended from the middle of a uniform rod which passes over two fixed supports 6 feet apart.   lu moving the body <> inches nearer to one of the supports the pressure on the support, increases by  100 pounds.   What is the weight of the body if 5 pounds is the weight of
the rod?                                                                      ,   t t
5.  A uniform rod of length a and weight II is suspended by two strings
having lengths li and k. The lower ends of the strings are at taehed to t he ends of the rod, while the upper ends are tied to a peg. Kind the tensile force in the strings.
6.   A safety valve consists of a cylinder with a plunger attached to a uniform bar hinged at one end.   The plunger lias a diameter of J inch and is attached to the bar at a distance of 1 inch from the* hinge,   The bar is 2 feet long and weighs 1 pound.   How far from the hinge must a slide-weight of 2 pounds be set if the steam is to blow off at 120 pounds per square inch?
7.   The two legs of a stepladder are hinged at the top and connected at the middle by a string of negligible mass.    Find the tensile force in the string and the pressure on the hinges when the. ladder stands on a smooth plane.   The weight of the ladder is W, the length of its legs /, and the length of the string a.
8.   A uniform rod rests on two smooth inclined planes making angles of ai and a2 with the horizon.   Find the angle which the rod makes with the horizon and the pressure on the planes.
9.   A rectangular block is placed on a rough inclined plane whose inclination is gradually increased.   If the block begins to slide* and to turn about its lowest edge simultaneously find the coefficient of friction.
10.   A uniform rod rests with one end against a rough vertical wall and the other end connected to a point in the wall by a .string of equal length.   Show that the smallest angle which the. string can make* with
/3\ the wall is tan""11 -1 
11.   A uniform rod is suspended by a string which is attached to the? ends and is slung over a smooth peg.   Show that in equilibrium tin* rwi is either horizontal or vertical.
12.   A ladder 25 feet long and weighing 50 pounds resin against a vertical wall making ,30 with it.   How high can a man weighing 150 pounds climb up the ladder before it begins to Blip?   The coefficient of friction is 0.5 at both ends of the ladder.
13.   A rod of negligible weight rests wholly inside a Hinooth hemispherical bowl of radius r.   A weight W is clamped on to the rod at a point whose distances from the ends are a and 6.   Show that the equilibrium